The study of dynamical instability (stability) of spherical stellar system shows
that for adiabatic index \(\Gamma <4/3\)  \(\left(\Gamma >4/3\right)\)  the stellar system becomes
unstable (stable) as the weight of the stellar system increase much faster
(remains less than) than that of its pressure [1]}.
Also, the causality condition imposes certain constraints on
the dynamics of the stellar system such that inside the star,
the radial \(V_{r}\)  and the transverse \(V_{t}\)  components of the
speed of sound should be less than
the speed of the light (\(c=1\) ), so that \(0\le V_{r}\le 1\)  and \(0\le V_{t}\le 1\)  [2]}.
Thus, to check the stability/instability of the collapsing stellar system,
we need to study the behavior of the important physical quantities,
adiabatic index, sound of the speed which are defined as [3]}, [2]}, [5]}
\(\Gamma _{eff}&=&\left[\frac{\partial ( \ln p_{r})}{\partial ( \ln \rho )}\right]_{\Sigma }=\left[\left(\frac{\dot{p}_{r}}{p_{r}}\right) \left(\frac{\dot{\rho }}{\rho }\right)\right]_{\Sigma }\\Vr&=&\frac{d\,p_{r}}{d\rho }\,\, ,\hspace{28.45274pt}Vt=\frac{d\,p_{t}}{d\rho }\) 
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